Solvability of a problem on the plane motion of a heavy viscous incompressible capillary liquid partially filling a container

The solvability of a plane stationary boundary value problem for the Navier–Stokes system of equations describing the motion of a viscous incompressible capillary liquid with a free surface is proved. It is assumed that the free surface maintains contact with the wall of the container holding the liquid.
Bibliography: 21 titles.